{
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  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a4cb1cd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %matplotlib inline  #使用python 的matplotlib包来画图\n",
    "import random \n",
    "import torch \n",
    "from d2l import torch as d2l\n",
    "\n",
    "def synthetic_data(w, b, num_examples):\n",
    "    '''生成y  = x2 + b + 噪声'''\n",
    "    x = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(x, w) + b #矩阵乘法，多维时会有广播机制更复杂\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    return x, y.reshape((-1, 1))\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "511a9d3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feature: tensor([ 1.2768, -0.7397]) \n",
      "label: tensor([11.5386])\n"
     ]
    }
   ],
   "source": [
    "print('feature:', feature[0], '\\nlabel:', labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0083512e",
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, 1].detach().numpy(),\n",
    "                labels.detach().numpy(),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5905b49e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i:min(i + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]\n",
    "batch_size = 10"
   ]
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  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2b162844",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 2.0411, -0.9557],\n",
      "        [-1.2089,  1.3564],\n",
      "        [-1.0224, -0.0900],\n",
      "        [ 0.8416, -0.8580],\n",
      "        [ 0.9018, -0.0925],\n",
      "        [-1.1548, -0.4790],\n",
      "        [ 0.2683,  0.4666],\n",
      "        [-0.2089, -1.5897],\n",
      "        [-0.2208,  1.6639],\n",
      "        [ 0.0792, -0.6384]]) \n",
      " tensor([[11.5386],\n",
      "        [-2.8492],\n",
      "        [ 2.4766],\n",
      "        [ 8.7919],\n",
      "        [ 6.3132],\n",
      "        [ 3.5178],\n",
      "        [ 3.1414],\n",
      "        [ 9.1693],\n",
      "        [-1.9047],\n",
      "        [ 6.5360]])\n"
     ]
    }
   ],
   "source": [
    "for x, y in data_iter(batch_size, features, labels):\n",
    "    print(x, '\\n', y)\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "133c0886",
   "metadata": {},
   "outputs": [],
   "source": [
    "w = torch.normal(0, 0.01, size= (2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "39e93cd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(x, w, b):\n",
    "    \"\"\"线性回归\"\"\"\n",
    "    return torch.matmul(x, w) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fd865ab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def squard_loss(y_hat, y):\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 /2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31691643",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad():\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size\n",
    "            param.grad.zero_()"
   ]
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